When we consider plastic materials, we have a yield function F. While the plastic flow is assumed nonassociated, we further have a plastic potential usually represented by G. My question is that why F and G usually have a similar format. For instance, in nonassociated Mohr-Coulomb model, the only difference between F and G is that one uses friction angle while the other dilation angle. Are there any theories behind it or is it just for convinience?
Strictly speaking, this equivalence between F and G is valid only for highly ductile materials. The author of a rather comprehensive theoretical study on this issue (attached) comes to conclusion that the dilatational contributions to G and F are quite different leading to a substantial inequivalence between the two. Take a look.
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